The lines r→=a→+λ(b→×c→)  and r→=b→+μ(c→×a→) will intersect if

The lines r→=a→+λ(b→×c→)  and r→=b→+μ(c→×a→) pass through points a→ and b→respectively, and are parallel to the vectors  b→×c→ and c→×a→ , respectively. Therefore, they intersect if a→−b→,b→×c→ and c→×a→ are coplanar and so(a→−b→)⋅{(b→×c→)×(c→×a→)}=0or  (a→−b→)⋅([b→c→a→]c→−[b→c→c→]a→)=0or  ((a→−b→)⋅c→)[b→c→a→]=0or  a→⋅c→−b→⋅c→=0 or a→⋅c→=b→⋅c→